In the research of QSAR and QSPR correlations, topological indices such as Randi’c index, Zagreb ABC geometric-arithmetic index have been proposed to analyze bio-compatibility chemical compounds. Chemical graph theory is combination Chemistry Graph theory, this deals with topology mathematical study isomerism development which has applications in QSPR. article, we consider Octahedron networks f...

This paper proposes arithmetic and geometric Paasche quality-adjusted price indexes that combine micro data from the base period with macro data on the averages of asset prices and characteristics at the index period. The suggested index has two types of advantages relative to traditional Paasche indexes: (i) simplification and cost reduction of data acquisition and manipulation; and (ii) poten...

The paper discusses the asymptotic behavior of generalizations of the Gauss’s arithmetic-geometric mean, associated with the names Meissel (1875) and Borchardt (1876). The "hapless computer experiment" in the title refers to the fact that the author at an earlier stage thought that one had genuine asymptotic formulae but it is now shown that in general "fluctuations" are present. However, no ve...

This paper proposes the development of an index to assess rural based on a set 25 demographic, economic, environmental, and social welfare indicators previously selected through Delphi approach. Three widely accepted aggregation methods were then tested: mixed arithmetic/geometric mean without weightings for each indicator; weighted arithmetic using weights generated by panel Principal Componen...

in this study, some seed physical properties of two sugar beet varieties, shirin and gadouk (436), were evaluated as a function of moisture content. physical properties included length, width, thickness, arithmetic and geometric mean diameters, sphericity, thousand seed weight, angle of repose, terminal velocity, true density, bulk density, porosity, and coefficient of friction. four moisture c...

This course will consist of two parts with the common theme of analyzing a geometric object via geometric sub-objects which are ‘small’ in an appropriate sense. In the first half of the course, we will begin by describing the work on H. W. Lenstra, Jr., on finding generators for the unit groups of subrings of number fields. Lenstra discovered that from the point of view of computational complex...

In this article we prove a generalization of Selberg’s lemma on the existence of torsion free, finite index subgroups of arithmetic groups. Some of the geometric applications are the resolution a conjecture of Nimershiem and answers to questions of Long–Reid and the author.